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Abstract

Amplification of signals is an elemental function for many information processing systems and communication networks. However, optical quantum amplification has always been a technical challenge in both free space and fiber optics communication. Any phase-insensitive amplification of quantum light states would experience a degradation of signal-to-noise ratio as large as 3 dB for large gains. Fortunately, this degradation can be surmounted by probabilistic amplification processes. Here we experimentally demonstrate a linear amplification scheme for coherent input states that combines a heralded measurement-based noiseless linear amplifier and a deterministic linear amplifier. The amplifier is phase-insensitive and can enhance the signal-to-noise ratio of the incoming optical signal. By concatenating the two amplifiers, it introduces flexibility that allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between these performances and a finite heralding probability. We demonstrate amplification with a signal transfer coefficient of Ts>1 with no statistical distortion of the output state. By partially relaxing the demand of output Gaussianity, we can obtain further improvement to achieve a Ts=2.55±0.08 with an amplification gain of 10.54. Since our amplification scheme only relies on linear optics and a post-selection algorithm, it has the potential of being used as a building block in extending the distance of quantum communication.

Supplementary Material (1)

Supplemental document containing (1) our experimental scheme; (2) the derivation of the success probability; (3) the theoretical model that takes into account the experimental imperfections; and (4)Fig. S2, which plots the signal transfer coefficient as a function of power gain for two conjugate quadratures, as mentioned in Sec. 4B.

Figures (6)

Fig. 1. Wigner function contours of input and output coherent states for a continuum of linear amplifiers. The green dashed circle here refers to the best possible deterministic linear amplifier, which adds the minimum amount of noise imposed by quantum mechanics; any amplifier that introduces less noise is necessarily probabilistic. One example of the probabilistic amplifiers is the perfect linear amplifier (PLA) that preserves the SNR of an incoming signal while amplifying its power. Amplifiers capable of enhancing SNR are called noise-reduced amplifiers (shaded area in orange, including the NLA) and the extreme case of the noise-reduced amplifier is an NLA that not only amplifies the amplitude of an input state, but also preserves its noise characteristics.

Fig. 3. Tunability of the amplifier. Signal transfer coefficient (blue contours), various effective gains (red contours), and T′ (green lines) as the function of gNLA and gDLA. The blue-dotted line denotes the amplification process where the input SNR is preserved, while the enclosed shaded area refers to the region where additional noise is introduced. We note that, without a sufficiently high NLA gain, increasing gDLA alone would not suffice to approach the noise-reduced amplification.

Fig. 4. Linearity of the amplifier. (a) Amplification for coherent states with different amplitudes. Left panels: noise contours (one standard deviation width) of the amplified states, depicted in red. Right panels: normalized probability distribution for amplitude and phase quadratures of the output states. (b) Output magnitudes versus input magnitudes as we reduce the cutoff while maintaining the values of gNLA′ and gDLA′. Inset: output magnitudes versus input magnitudes with cutoff αc=4.42 at different effective gains.

Fig. 5. Amplifier performance: noise properties and contour plot of the success probability PS in logarithmic scale as a function of Ts and geff. The success probability decreases as we increase the effective gain. The signal transfer coefficient for amplitude quadrature (blue symbols) is also superimposed as a function of geff2 for varying T′: 0.6, 0.45. The theoretical prediction, assuming infinite cutoff, is depicted in crosses. It is clearly shown that the experimental Ts increases in compliance with the prediction, demonstrating that the cutoff (αc=4.3) selected is sufficient and no over- or underestimation of Ts appears. For the sake of comparison, the best achievable Ts of an optimal deterministic linear amplifier (also termed as the quantum noise limit) is shown in the orange solid line. This illustrates that our amplifier surpasses the quantum limit for a phase-insensitive amplifier, and this superiority becomes more distinguished as we increase the geff. Inset: the experimental data superimposed with its theoretical prediction for phase quadrature.

Fig. 6. Signal transfer coefficients in the large gain domain. (a) Ts exceeding 1 with increasing geff for αc=4.5 and a coherent state amplitude of |α|=0.5. The experimental Ts shows good agreement with the theory plot (in crosses) until around geff=6.5, where the data points start to depart, thereby indicating that the cutoff no long suffices to maintain the output Gaussianity. Inset: probability distribution of the amplified state labeled in red. (b) Probability distributions of the phase quadrature of the amplified state with cutoffs given by Eq. (15). Data points are the post-selected ensemble out from 2.7×109 homodyne measurements, while the red curves indicate the corresponding best-fitted Gaussian distributions.